GPS World, January 2009

INNOVATION Receiver Technology channel Traditional 4 Skimmer and architecture distiller architecture Sk0 Ds0 Ds1 Ds2 Ds3 Ch0 Ch1 Ch2 Ch3 4 8 12 16 Faster than 2 channels T0 T1 T2 Faster than 3 channels 18 searches processed by the skimmer 20 searches executed by the 4 channels Å FIGURE 3 Candidate selection process timeline for skimmer and distiller and reference architectures 100000 10000 1000 100 10 0 90 confidence 99 confidence 50 100 150 200 250 300 Number of noncoherent accumulations 1 Rank Å FIGURE 4 90 and 99 percent rankings as a function of the integration time expressed as the number of noncoherent accumulations N T where T is the 16 millisecond coherent integration interval 100 80 60 40 20 0 1 4 16 128 256 512 1024 0 50 100 150 200 Cumulative probability percent Number of noncoherent accumulations Å FIGURE 5 Measured ranking performance for a signal at 155 dBmW from the skimmer process for different numbers of candidates Skimmers and distillers have very different architectures In a skimmer the search is over a continuous region while the distillers in general will operate on a noncontinuous region of the search space with the candidate positions uniformly spread over the uncertainty region For the case of nominal flow no anomalies are detected the process stops whenever the last stage is capable of producing a number of candidates equal to or less than the number of tracking channels available in the receiver for confirmation Both skimmers and distillers use the magnitude of the noncoherent accumulations on every correlator tap as a likelihood estimator Ranking To measure the performance of the candidate selection phase of the satellite search and acquisition function we need to define the statistical parameter called Rank p where p is a particular probability level Given an integration interval T under the hypothesis that a signal is present the signal is included in the search region the acquisition engine selection algorithm determines a list of candidates in descending order of probability Let R be the cumulative distribution function of the rankings that is the position in the sorted list of the nearest tap to the signal in this sorted list This tap will be referred to as the best tap A rank equal to one means that the acquisition engine has selected as first choice the most likely candidate the tap aligned with or closest to the real signal Rank p is defined as Rank p R p 4 If an acquisition engine has Rank 09 4 for a period T with a signal whose C N 0 is equal to C this means that in 90 percent of the trials the acquisition engine will be able to select the best tap among the four best candidates FIGURE 4 shows plots of the Rank 09 and Rank 099 statistics for the following conditions a signal at 15 dB Hz C a searchspace uncertainty of 8 frequency bins F a code phase uncertainty of 512 chips and a coherent integration interval of 16 milliseconds T In total 16368 taps are needed to cover the uncertainty region 1023 2 8 In practice 8 channels of the reference architecture are used The plots in Figure 4 show the Rank 09 and Rank 099 values of the best tap as a function of the noncoherent integration interval when the desired signal is present The horizontal axis in Figure 4 can thus be viewed as the number of noncoherent integrations that have taken place while the vertical axis indicates the rank on a logarithmic scale Figure 4 shows how in general a massive correlator approach is inefficient in terms of resource usage It suggests that after 270 accumulations we can select correctly the best tap but after just 70 accumulations we can with the same confidence say that 90 percent of the taps are tracking noise that is only 10 percent of the tap resources are used efficiently The estimate of the ranking distribution at a particular C N 0 level is based on simple statistics with the results of the noncoherent accumulation of the correlations Y being modeled as a stochastic variable with a chi squared 2 distribution in the case where no signal is present and a noncentral 2 distribution in the case where a signal is present To completely define the distributions of Y for the signal and noise cases we need two parameters the degrees of freedom and the noncentrality parameter Since the input signal has two components real and imaginary or in phase and quadrature in both cases the degrees of freedom is set at two times the number of accumulations Given the signal C N 0 the noncentrality parameter of the noncentral 2 distribution can be readily computed see GPS World January 2009 www gpsworld com 42

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